Abstract: The classical online rental problem only considers two options:buy or rent.This paper assumes that the buying-permission can be canceled,and proposes the online rental problem with canceling buying -permission.The proposed problem is a generalization of the classical online rental problem.Using the method of traditional competitive analysis,we design the optimal investment strategy for this problem.Moreover,we also give the optimal strategies under the risk-reward framework.These results can provide a basis for further constructing the framework of the online leasing problem based on contracts.

Key words: online rental problem, competitive analysis, risk-reward model